With the approximation in (REF ), the proposed joint precoding framework can be also used in non-ideal ris cases \({\cal F}_2\)  and \({\cal F}_3\)  as well. It should be pointed out that, since the loss caused by the approximation might be large and hard to estimate, some other discrete optimization methods such as ace algorithm [1]} might be used to alleviate the approximation loss in the non-ideal ris cases, which is left for future work.
